The Earth can be considered an inertial frame of reference in the Newtonian sense, where gravity is a real force, and when you disregard it's rotation about its axis as well as its rotation about the Sun and the Sun's rotation about the Galactic center.

I don't see how you could consider the whole Earth as an inertial frame of reference, but only a tiny part of it (or an object of its surface). As soon as you take into account the whole planet, you can't ignore the fact that it's moving, both transating and especially rotating.

If the time and space scales of your motion are very short (e.g., throwing a ball over normal, human distances) then the trajectory will barely be affected by the earth's rotation. Just imagine how far the earth will have rotated under your ball during the time it was in the air.

If you're firing naval artillery shells that can fly for more than a minute and disappear over the horizon, then yes you need to consider the rotation of the earth.